From divots to swales: Hillslope sediment transport across divers length scales
Article first published online: 2 JUL 2010
Copyright 2010 by the American Geophysical Union.
Journal of Geophysical Research: Earth Surface (2003–2012)
Volume 115, Issue F3, September 2010
How to Cite
2010), From divots to swales: Hillslope sediment transport across divers length scales, J. Geophys. Res., 115, F03001, doi:10.1029/2009JF001576., and (
- Issue published online: 2 JUL 2010
- Article first published online: 2 JUL 2010
- Manuscript Accepted: 29 JAN 2010
- Manuscript Revised: 8 JAN 2010
- Manuscript Received: 26 OCT 2009
- sediment transport;
- master equation;
- Fokker-Planck equation
 In soil-mantled steeplands, soil motions associated with creep, ravel, rain splash, soil slips, tree throw, and rodent activity are patchy and intermittent and involve widely varying travel distances. To describe the collective effect of these motions, we formulate a nonlocal expression for the soil flux. This probabilistic formulation involves upslope and downslope convolutions of land surface geometry to characterize motions in both directions, notably accommodating the bidirectional dispersal of material on gentle slopes as well as mostly downslope dispersal on steeper slopes, and it distinguishes between the mobilization of soil material and the effect of surface slope in giving a downslope bias to the dispersal of mobilized material. The formulation separates dispersal associated with intermittent surface motions from the slower bulk behavior associated with small-scale bioturbation and similar dilational processes operating mostly within the soil column. With a uniform rate of mobilization of soil material, the nearly parabolic form of a hillslope profile at steady state resembles a diffusive behavior. With a slope-dependent rate of mobilization, the steady state hillslope profile takes on a nonparabolic form where land surface elevation varies with downslope distance x as xa with a ∼ 3/2, consistent with field observations and where the flux increases nonlinearly with increasing slope. The convolution description of the soil flux, when substituted into a suitable expression of conservation, yields a nonlinear Fokker-Planck equation and can be mapped to discrete particle models of hillslope behavior and descriptions of soil-grain transport by rain splash as a stochastic advection-dispersion process.